theorem
  ex P being permutational non empty set st len P =n
proof
  set p = the Permutation of Seg n;
  set P={p};
  now
    take n;
    let x;
    assume x in P;
    hence x is Permutation of Seg n by TARSKI:def 1;
  end;
  then reconsider P as permutational non empty set by Def10;
  take P;
  len P= n
  proof
    set x = the Element of P;
    reconsider y=x as Function of Seg n,Seg n by TARSKI:def 1;
A1: dom y=Seg n by FUNCT_2:52;
    then reconsider s=y as FinSequence by FINSEQ_1:def 2;
    n in NAT & len P= len s by Def11,ORDINAL1:def 12;
    hence thesis by A1,FINSEQ_1:def 3;
  end;
  hence thesis;
end;
